﻿using System.Collections.Generic;

namespace ProblemsSet
{
    public class Problem_74 : BaseProblem
    {
        public override object GetResult()
        {
            const int max = 1000000;

            long res = 0;
            for (long n = 1; n < max; n++)
            {
                var tmp = new List<string>() {n.ToString()};
                MathLogic.IsNonRepeating(ref tmp, 61);
                if (tmp.Count == 60)
                    res++;
            }
            return res;
        }

        public override string Problem
        {
            get
            {
                return @"The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:

1! + 4! + 5! = 1 + 24 + 120 = 145

Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:

169  363601  1454  169
871  45361  871
872  45362  872

It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,

69  363600  1454  169  363601 ( 1454)
78  45360  871  45361 ( 871)
540  145 ( 145)

Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.

How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?";
            }
        }

        public override bool IsSolved
        {
            get
            {
                return true;
            }
        }

        public override object Answer
        {
            get
            {
                return 402;
            }
        }

    }
}
